the Mind of BTK:
The True Story Behind the Thirty-Year Hunt for the Notorious Wichita Serial Killer
by John Douglas
For some stocks, you can buy something called "options." An option is a little bit like an insurance policy or a warranty. For more info about options, visit www.cboe.org.
Like casinos in Vegas, option sellers want to set prices and conditions on options that will fix the odds and limit their risk of losing money. One of the most famous tools(since 1973) for calculating theoretical option price (T.O.P.) is the:
"Nobel Prize winning Black Scholes Formula"
|P = stock price
S = striking price
V = volatility
r = current risk free interest rate
t = time (percent of a year)
N(d) = cumulative normal distribution function
(The latter is a separate formula or algorithm.) N(d) gives you (in%) the probability of a stock's price being above, below (or at) a given value at a future point in time. This N(d) is sometimes called the "hedge ratio."
On the next pages, I'll show 2 ways to not only combine the N(d) and Black-Scholes formulas into a single formula, but also to simplify and shorten it.
|However, there is something that is more important to us than option price; we are interested in the figures that were used to calculate it, because these figures might tell us what the seller's "insider" information really was, i.e., how stable the stock is, or how well he really thought the stock (or the corporation) would perform.|
In fact, math whiz analysts especially like to figure out what original value of "V" was used. They call this "implied volatitlity."
|Here, we start with a guess for "V" (when the option price, T.O.P. is known), and this formula gives us a new "V" that is closer. You could use the new "V" (Vi+1) and repeat the process, but you wouldn't need to re-calculate W. Only d, Xa, and R.|
B. Special Circumstances: When you calculate "b" and "d" watch their signs. If both b & d become negative (both<0) at any point, you may switch over and use these even simpler versions of the formulas:
Here again (as with page 2) the first guess must be on the high side, like 50% (.5) or 80% (Vi = .8). The volatility of a stock tells us the probability (odds) that a stocks price will change in a given time period.
These formulas for implied volatility are my invention.
P.S. Let me explain in more detail why my formula is an improvement from the standard form.
FIRST, the N(d) and N(b) - sometimes written as N(d1) and N(d2) - refer to separate formulas or algorithms which simply calculate areas under the "bell" curve. This usually requires calculus; however, I've managed to combine this process with the rest of our formula and make it a purely algebraic task that anyone(who can use algebraic type formulas) can deal with.
SECOND, I have found a way to considerably simplify my combined algebraic form so that it can be solved faster than the standard form. This may not seem obvious to you at first, but to anyone who is indeed accustomed to using the Black-Scholes formula, it should be immediately apparent that it is shorter; however, my version is algebaically identical and yields the exact same(equal) results. Since this process often gets repeated hundreds of times, even a small improvement can save a lot of calculation time.
return to the picnic.
© copyright 1997 manson family picnic. all rights reserved.